The champions conceded a last-minute goal on Sunday when they were held to a surprise 2-2 home draw by bottom club Fulham and in their previous game slumped to a 2-1 defeat at Stoke City.
"You just continue doing the right things, we're doing the right things," said Moyes on Tuesday while also dismissing a media report that former England defender Rio Ferdinand would be quitting football at the end of the season.
"We just need to keep going because our luck will change, there's no doubt about that," the manager told the club website (www.manutd.com).
United, who trail leaders Chelsea by 15 points, are languishing in seventh position but did record a 1-0 victory over Arsenal on home soil in November thanks to a goal from former Gunners favourite Robin van Persie.
"We got a good result against them at Old Trafford and we'll try to do the same again," said Moyes who took over when Alex Ferguson retired at the end of last season.
"We are a top side and hopefully we'll go and show that tomorrow."
According to The Sun newspaper, Ferdinand was going to be left out of United's warm-weather training camp in Dubai later this week and that the centre half would be retiring at the end of the season.
"I can only tell you that what was written today was a load of rubbish, complete nonsense," said Moyes.
United are again expected to be without midfielder Marouane Fellaini and defenders Jonny Evans and Phil Jones against Arsenal who are second in the table, one point behind leaders Chelsea.
(Reporting by Mark Pangallo; editing by Tony Jimenez)
